10 ideas
8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |
8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
22591 | We know perfection when we see what is imperfect [Murdoch] |